Attacking (EC)DSA scheme with ephemeral keys sharing specific bits

In this paper, we present a deterministic attack on (EC)DSA signature scheme, providing that several signatures are known such that the corresponding ephemeral keys share a certain amount of bits without knowing their value. By eliminating the shared blocks of bits between the ephemeral keys, we get...

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Vydané v:	Theoretical computer science Ročník 1001; s. 114578
Hlavní autori:	Adamoudis, M., Draziotis, K.A., Poulakis, D.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 27.06.2024
Predmet:	Digital signature algorithm Elliptic curve digital signature algorithm Kannan's enumeration algorithm Lattice LLL algorithm Elliptic curve digital signature algorithm Digital signature algorithm LLL algorithm Lattice Kannan's enumeration algorithm
ISSN:	0304-3975, 1879-2294
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Popis
Shrnutí:	In this paper, we present a deterministic attack on (EC)DSA signature scheme, providing that several signatures are known such that the corresponding ephemeral keys share a certain amount of bits without knowing their value. By eliminating the shared blocks of bits between the ephemeral keys, we get a lattice of dimension equal to the number of signatures having a vector containing the private key. We compute an upper bound for the distance of this vector from a target vector, and next, using Kannan's enumeration algorithm, we determine it and hence the secret key. The attack can be made highly efficient by appropriately selecting the number of shared bits and the number of signatures.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2024.114578